Abstract
The Christoffel symbols of first and second kind that are used in the general theory of relativity via the Riemmanian differential geometry can be used also for the index zero formulation of mechanical systems that are defined in a multi-dimensional space. The formulation presents some advantages for numerical solution of the equations describing the dynamic behaviour of these systems. This paper harmonizes the relation between the numerical integration methods and dynamic formulation of the equation of motion, keeping in mind the robustness and accuracy of the numerical solutions. It is based on the results obtained in papers by Calahan, Gear, and Orlandea and Coddington. The formulation specifically refers to articulated mechanisms and planetary systems. However, it can be applied to any multi-degrees-of-freedom system for which the transmission functions can be defined as in the works of Maros and Orlandea. After the definitions of index and transmission functions are introduced and explained the formulation is implemented and applied to mechanisms. The results indicate that for systems such as planetary systems and articulated mechanisms, this method can be applied toward real-time digital simulation.
Published Version
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